How to Get Object's Coordinates to Display as 0,0,0 when Parented, and Update Transform Values as if Parent was at World Space Origin?
An example of object parenting
Object A has its origin in world space at x=10.0, y=10.0, z=10.0
Object B has its origin in world space at x=2.0, y=2.0, z=2.0
When parenting Object B to Object A, Object B ends up in the coordinate space of Object A.
The new coordinates of Object B in local coordinate space, relative to its parent, are: x=-8.0, y=-8.0, z=-8.0
What Blender displays in the UI
Blender does the exact same thing as described above.
Object B does end up in the coordinate space of Object A.
But the coordinates you see in the UI - in the item panel of the 3D view - are still displaying x=2.0, y=2.0, z=2.0. I guess you expected it to display the coordinates in local space like x=-8.0, y=-8.0, z=-8.0.
What you see in that place of the UI is the &quot;location&quot; tied to the so called &quot;Input Matrix&quot; resp. matrix_basis.
The &quot;Input Matrix&quot; is neither the global matrix nor the local matrix, but a particular matrix for user input. Citing the docs:

Matrix access to location, rotation and scale (including deltas),
before constraints and parenting are applied

https://docs.blender.org/api/current/bpy.types.Object.html#bpy.types.Object.matrix_basis
So it’s kind of an unspoilt matrix that is not &quot;polluted&quot; by constraints or parenting.
You could add a &quot;Limit Location&quot; constraint to Object B, limit its location to 0/0/0, but the input matrix remains on 2/2/2.
The &quot;location&quot; that is actually displayed in the UI is the input matrix without delta transforms.
On the one hand it’s a pretty clean and stable matrix to keep user input separate from other influences.
On the other hand I can understand that you’d like to see and edit the final/actual coordinates in local space after parenting.
Possible Solutions
Here’s a corresponding feature request with some discussion:
https://blender.community/c/rightclickselect/hLdbbc/
In there they’re mentioning an addon that adds direct access to world and local matrix in the object properties:
https://gitlab.com/blender3d/addons/object-location-edit/-/releases#v0.03
And here’s an addon that transforms the matrix values in a way that the values of the input matrix become those of the local matrix:
https://github.com/drewcassidy/blender-apply-parent-inverse
You can see and edit all these matrices without any plugin in the Outliner:

Set the Outliner’s display mode to &quot;Data API&quot;
Object -&gt; &quot;Object B&quot; -&gt; Matrix World / Local Matrix / Input Matrix / Parent Inverse Matrix

Checking out the local matrix you’ll see Object B's coordinates are: x=-8.0, y=-8.0, z=-8.0 indeed.